Method and system of estimating the cross-sectional area of a molecule for use in the prediction of ion mobility

ABSTRACT

A method of estimating the cross-sectional area of a molecule for use in the prediction of ion mobility gives gas phase interaction radii determination and cross-sectional algorithm computation to provide separation and characterization of structurally related isomers. More specifically, the invention provides a method of correlating the differences in the molecular structures with differences in anti-cancer activity of pre-determined anti-cancer drugs by utilizing a new algorithm for estimating the cross-sectional area of the molecules of such drugs.

This invention relates to a method of estimating the cross-sectionalarea of a molecule for use in the prediction of ion mobility for a widerange of molecular species.

Ion mobility has the potential to separate isomeric species based ondifferences in gas phase collision cross-sections (Ω) and can providevaluable information on ionic conformation through comparisons withtheoretical models. However, to relate the ion mobility derivedcollision cross-section of a molecule to its structure accurately, it isnecessary to obtain prior knowledge of the gas phase radii of theconstituent atoms.

The molecular cross-section is approximated as the rotationally averagedarea of the “shadow” cast by the molecule. The term “shadow” is used torefer to the projection of a molecule, atom or ellipsoid onto any plane.The plane employed remains fixed throughout the calculation.

The projection approximation (PA) has been shown to be a useful methodof calculating the cross-section of a molecule to be used in theprediction of ion mobility. It is not possible to calculate theprojection approximation cross-section directly, but it is possible toobtain numerical approximations using Monte Carlo techniques. MonteCarlo methods are a class of computational algorithms that rely onrepeated random sampling to compute their results and often are usedwhen it is infeasible or impossible to compute an exact result with adeterministic algorithm.

It is known to obtain prior knowledge of the gas phase radii of theconstituent atoms of a molecule by means of an algorithm known as MobCal(http://www.indiana.edu/˜nano/Software.html) which includes thefollowing steps:—

(1) Set A = O, n = O, and (2) select a random orientation of themolecule (3) select a rectangle bounding the molecular shadow andcalculate the area of the rectangle = area Abox, (4) select a pointrandomly within the rectangle, (5) if the point lies within themolecular shadow, then A = A + Abox (6) n = n + 1 (7) if n < n_(max)GOTO 2 (i.e. select another random orientation of the molecule for thenext iteration) (8) End. Result is A/n

However, there are at least two potential (but related) problems withthis approach. First, in the selection of n_(max), it is difficult ifnot impossible to know how many orientations (step 2) are sufficient,and secondly there are situations in which convergence is slow so thatnaive convergence tests can be misleading.

The above algorithm can be improved to allow more than one selection perorientation giving a modified algorithm

One aspect or feature of the invention provides a method of estimatingthe cross sectional area of a molecule, e.g. for determining thecharacteristics of predetermined or sample molecules, the method thesteps of:

(1) Set A = O, n = O, and (2) select a random orientation of themolecule (3) select a rectangle bounding the molecular shadow andcalculate the area of the rectangle = area Abox (4) select K pointsrandomly within the rectangle (5) for each point that lies in themolecular shadow, A = A + Abox/K (6) n = n + 1 (7) if n < n_(max) GOTO 2(next iteration) (8) End. Result is A/n

The above method will be referred to hereinafter as the ‘rectangle’method.

However, the present invention also involves the use of a newlydeveloped collisional cross-sectional (CCS) algorithm which is a highlyefficient implementation of the projection approximation that utilises anovel sampling technique to provide improved confidence in convergenceof the rotationally averaged cross section, obtained to a user-specifiedaccuracy.

Another aspect of the present invention provides a method of estimatingthe cross sectional area of a molecule, e.g. for determining thecharacteristics of predetermined or sample molecules, the methodcomprising the steps of:

-   -   A) Predicting the geometric structure of the molecule of        interest;    -   B) Assigning a value for the cross sectional area of each atom        within the molecule;    -   C) Calculating the sum of the values of the cross sectional area        for each atom within the molecule;    -   D) Randomly selecting an orientation of the predicted geometric        structure of said molecule of interest;    -   E) Randomly selecting one or more atoms with probability        proportional to the atoms cross sectional area;    -   F) Randomly selecting a position within the cross sectional area        of the, or each of, the selected atom(s);    -   G) Identify the number of atoms whose cross sectional area        includes said randomly selected position;    -   H) Calculating a value for the cross sectional area of said        molecule of interest at said randomly selected orientation;    -   I) Calculate an averaged cross sectional area over all said        randomly selected orientations;    -   J) Iterate steps D) to I) for at least N iterations and/or until        M independent calculations of the averaged cross sectional area        agree within a predetermined range R for X iterations

The above method will be referred to hereinafter as the ‘importancesampling’ method.

According to a feature of the invention the value of N may be between 0and 50, for example between 0 and 30 or between 20 and 50 or between 10and 40.

According to another feature of the invention the value of M may bebetween 1 and 20, for example between 1 and 10 or 1 and 5 oralternatively between 10 and 20 or 15 and 20 or alternatively between 5and 15.

According to another feature of the invention the value of R may bebetween 0.1 and 20%, for example 1 and 20% or alternatively between 0.1and 1%.

[Note that R can be a percentage or an absolute value]

According to another feature of the invention the value of X may bebetween 1 and 20, for example between 1 and 10 or 1 and 5 oralternatively between 10 and 20 or 15 and 20 or alternatively between 5and 15.

Another aspect of the invention provides a method of determiningcharacteristics of predetermined molecules (e.g. small molecules andproteins, peptides, oligoneucleotides and glycans) comprising the use ofa combined ion mobility—mass spectrometry (IM-MS) technique forexperimentally determining a range of molecular structures and comparingvalues of that range with those derived by an estimating methodaccording to any of the five immediately preceding paragraphs so as tocorrelate the differences in the molecule structures with differences inselected predetermined activity of those molecules.

According to a feature of this aspect of the invention, the method maycorrelate the differences in the molecular structures with differencesin anti-cancer activity of predetermined anti-cancer drugs. Preferably,the anti cancer drugs are organometallic based drugs. Preferably, theorganometallic drugs are isomeric Ru-based.

According to another feature of this aspect of the invention, the IM-MStechnique may include the use of travelling wave (T-wave) mobilityseparation.

The method of the present invention gives gas phase interaction radiidetermination and cross-section algorithm computation to provideseparation and characterisation of structurally related isomers by ionmobility.

A further aspect of the invention provides a system for determiningcharacteristics of predetermined molecules, the system comprising an ionmobility cell, a mass spectrometer and a processor programmed orconfigured to determine experimentally a range of molecular structuresand compare values of that range with those derived by an estimating amethod described above so as to correlate the differences in themolecular structures with differences in selected predetermined activityof those molecules.

A yet further aspect of the invention provides a computer programelement comprising computer readable program code means for causing aprocessor to execute a procedure to implement the method describedabove.

The computer program element may be embodied on a computer readablemedium.

A yet further aspect of the invention provides a computer readablemedium having a program stored thereon, where the program is to make acomputer execute a procedure to implement the method as described above.

An embodiment of the invention will now be described, by way of exampleonly, with reference to the accompanying drawing, wherein:

FIG. 1 is a flow chart illustrating an algorithm according to anembodiment of the present invention.

One algorithm of the present invention is as follows:—

(1) Amax = sum over π*R_(i)* R_(i) wherein R_(i) is the radius of thei'th atom (2) Set A = 0, n = 0, and (3) then select a random orientationof the molecule (4) select K atoms at random with probabilityproportional to the atom's cross sectional area (5) then select a pointwith uniform probability within the circular shadow of each selectedatom, and (6) for each thus selected point, A = A + Amax/(m*K) Where mis the number of atoms with shadows overlapping the point (7) n = n + 1(8) if n < n_(max) GOTO 3 (next iteration) (9) End. Result is A/n

For many molecules, this importance sampling algorithm will converge tothe desired result faster than that of the prior art algorithms referredto.

The following termination procedure has been implemented in conjunctionwith the above algorithm:—

-   (1) Instantiate N projection approximation calculations (henceforth    called objects)-   (2) perform iterations for each of these objects in turn, keeping    running area estimates for each object,-   (3) terminate when the area estimates for all objects agree with a    user specified tolerance (either percentage or absolute), reporting    the overall average of these estimates as the result.

It may be advantageous to use a mixture of objects utilizing both theprior art algorithms referred to and the algorithm of the presentinvention to achieve confidence in the termination.

This newly developed CCS algorithm is a highly efficient implementationof the projection approximation that utilises a novel sampling techniqueto provide improved confidence in convergence of the rotationallyaveraged cross section, obtained to a user-specified accuracy.

The IMS device of a mass spectrometer was calibrated using a haemoglobinpeptide mixture and other compounds of known collisional cross section,such as polyglycine(http://www.indiana.edu/˜clemmer/Research/research.htm); a calibrationcoefficient was then derived. The ion mobility of each small moleculewas measured and therefore the experimental collision cross sectiondetermined. The radius of each of the atoms, specific to an individualsmall molecule were then “tuned” within the CCS algorithm such that theoutput of the CCS algorithm closely matched the experimentally derivedCCS values for each of the small molecules analysed. An optimalinteraction radius value ({acute over (Å)}²) for C, H, O, S, CI, F, N &Ru were thus derived.

The small molecules used to optimise the CCS algorithm were: C60, C70,pyrene, camphene, phenanthrene, triphenylene, naphthalene, ampicillin,spermine, lorazepam, caffeine, reserpine, raffinose, nifedipine,nimodipine, dexamethazone, diphenylhydramine, metoprolol, glutathione,cysteine, apomorphine, erythromycin, oxytetracyclin, verapamil,salbutamol, acetylsalicylic acid, the 20 naturally occurring commonamino acids, angiotensin II, oxytocin, testosterone, ibuprofen,beta-cyclodextrin and the ruthenium containing compounds ru-ortho (andassociated HCI neutral loss species), ru-meta (and associated HCIneutral loss species), ru-para (and associated HCI neutral lossspecies).

Ion mobility-mass spectrometry combined with molecular modelling for theseparation and configurational analysis of low-molecular-weight isomericorganoruthenium anticancer complexes were separated using ion mobilitybased on travelling-wave technology and the experimentally determinedcollision cross sections were compared to theoretical calculations.

Certain organometallic drugs are used in the fight against cancer. Theplatinum-based drug, cisplatin [cis-diamminedichloridoplatinum(II)], forexample, falls into this category and is one of the leading drugs usedin the fight against cancer. DNA is a potential target for manymetal-based anticancer drugs and distortions of DNA structure oftencorrelate with anticancer activity. Other metal-based anticancer drugs,such as those based on ruthenium, are being developed as alternativetreatments to combat cancer. In particular, the aim is to widen thespectrum of anticancer activity, reduce unwanted side effects, and avoidcross-resistance with cisplatin and related drugs. Insights into thephysical size and shape of these novel Ru-based drugs are important forelucidation of structure-activity relationships and for optimizing keyinteractions such as intercalation into DNA. Three novel isomericRu-based anticancer drugs have been explored using a combined ionmobility and mass spectrometry (IM-MS) approach together with anestimating method according to the invention.

As a stand-alone technique, MS cannot separate isomeric species orprovide bulk structural conformational information. However, IM has theability to rapidly separate isomeric species (on the MS acquisitiontimescale) based on differences in their collision cross sections (CCS;physical size and shape) in the gas phase, thus providing specificinformation on ionic configuration. The combination of IM with MSprovides an extremely powerful analytical tool.

To investigate the possible benefits of the IM-MS technique, aninstrument that is based around “traveling-wave” (T-wave) mobilityseparation was used to analyze a mixture of three low-molecular-weightisomeric ruthenium terphenyl anticancer complexes (m/z 427.1 based on¹⁰²Ru). Individual differences in shape have been studied in an attemptto correlate them with differences in anticancer activity. Molecularmodelling was also used to generate a range of possible structures andthe theoretical CCSs for these structures were calculated for comparisonwith experimentally derived T-wave values. Excellent agreement wasobserved between the experimentally and theoretically derived CCSmeasurements.

The ion mobility derived gas phase interaction radii in combination withthe new CCS algorithm, molecular modelling and ion mobility massspectrometry for the separation and conformational analysis of threelow-molecular-weight isomeric organoruthenium anti-cancer complexescontaining ortho-, meta- or para-terphenyl arene ligands (Mw 427.1) andthe subsequent isomeric HCI neutral loss species (Mw 391.1) has beenused in accordance with the invention. The six isomeric compounds showedwell defined arrival time distributions allowing experimental collisioncross-sections to be calculated and compared to theoretical values.Excellent agreement was observed between all experimentally- andtheoretically-derived results. The difference in shape of the elongatedterphenyl arene compared to the more compact shapes is likely to make animportant contribution to the significantly higher anti-cancer activityof the elongated structure.

In summary, the invention reports inferred gas phase interaction radiifor H, C, and the previously uninvestigated O, S, CI, F, N, Fe, Pt andRu. Furthermore, the method of the present invention demonstrates forthe first time that isomeric ruthenium (II) terphenyl anticancercomplexes, whose CCSs differ by less than 9.0 {acute over (Å)}², can beseparated and characterised by travelling wave ion mobility.

The table below shows results that were obtained using the Mobcalalgorithm as compared with the rectangle and importance samplingmethods.

Compound Rectangle Importance Sampling Caffeine 0.050 seconds 0.016seconds Ampicillin 0.042 seconds 0.031 seconds Spermine 0.090 seconds0.013 seconds

It will be appreciated by those skilled in the art that any number ofcombinations of the aforementioned features and/or those shown in theappended drawing provide clear advantages over the prior art and aretherefore within the scope of the invention described herein.

The invention claimed is:
 1. A method of estimating the cross sectionalarea of a molecule of interest comprising the steps of: A) Developing apredicted geometric structure of the molecule of interest; B) Assigninga value for a cross sectional area of each atom within the molecule; C)Calculating a sum of values of the cross sectional area for each atomwithin the molecule; D) Randomly selecting an orientation of thepredicted geometric structure of said molecule of interest; E) Randomlyselecting a number of atoms K with a probability proportional to theatom's cross sectional area; F) Randomly selecting a position within thecross sectional area of each of the number of atoms K; G) Identifying anumber of atoms m whose cross sectional area includes said position; H)Calculating a value for the cross sectional area of said molecule ofinterest at said orientation based on the sum of values of the crosssectional area for each atom within the molecule divided by the numberof atoms K times the number of atoms m; I) Calculating an averaged crosssectional area over all said randomly selected orientations wherein atleast steps H) and I) are preformed with an sufficiently programmedcomputer; and J) Iterating steps D) to I) for at least N iterations oruntil M independent calculations of the averaged cross sectional areaagree within a predetermined range R for X iterations.
 2. A methodaccording to claim 1, wherein the value of N is between 1and
 50. 3. Amethod according to claim 1, wherein the value of M is between 1and 20.4. A method according to claim 1, wherein the value of R is between 1and 20%.
 5. A method according to claim 1, wherein the value of X isbetween 1and
 20. 6. A method of determining characteristics ofpredetermined molecules comprising: utilizing a combined ionmobility-mass spectrometry (IM-MS) technique for experimentallydetermining a range of molecular structures; and comparing values of therange with those derived by a method of estimating a cross-sectionalarea of a molecule of interest so as to correlate differences in themolecular structures with differences in selected predetermined activityof those molecules wherein said method of estimating the cross sectionalarea of a molecule of interest comprising the steps of: A) Developing apredicted geometric structure of the molecule of interest; B) Assigninga value for a cross sectional area of each atom within the molecule; C)Calculating a sum of values of the cross sectional area for each atomwithin the molecule; D) Randomly selecting an orientation of thepredicted geometric structure of said molecule of interest; E) Randomlyselecting a number of atoms K with a probability proportional to theatom's cross sectional area; F) Randomly selecting a position within thecross sectional area of each of the number of atoms K; G) Identifying anumber of atoms whose cross sectional area includes said position; H)Calculating a value for the cross sectional area of said molecule ofinterest at said orientation based on the sum of values of the crosssectional area for each atom within the molecule divided by the numberof atoms K times the number of atoms m; I) Calculating an averaged crosssectional area over all said randomly selected orientations; and J)Iterating steps D) to I) for at least N iterations or until Mindependent calculations of the averaged cross sectional area agreewithin a predetermined range R for X iterations wherein at least stepsD) to I) are preformed with an sufficiently programmed computer.
 7. Amethod according to claim 6 wherein the method correlates thedifferences in the molecular structures with differences in the activityof drugs.
 8. A method according to claim 7 wherein said drugs areorganometallic based drugs.
 9. A method according to claim 8 whereinsaid organometallic based drugs are anti-cancer drugs.
 10. A methodaccording to claim 8 wherein the organometallic based drugs are isomericRu-based.
 11. A method according to claim 6 wherein the IM-MS techniqueincludes the use of travelling wave (T-wave) mobility separation.
 12. Acomputer program element comprising computer readable program code meansfor causing a processor to execute a procedure to implement the methodof claim
 1. 13. Computer program element according to claim 12 embodiedon a computer readable medium.
 14. A computer readable medium having aprogram stored thereon, where the program is to make a computer executea procedure to implement the method of claim 1.